The subject of time travel is no stranger to the world of anime, so it takes a lot of work to make a time travel story stand out. For Steins;Gate, that hard work paid off. This is by far the best-executed time travel story that I've ever seen in my experience with anime, and if you haven't seen it yet, you're definitely missing out!
The story revolves around the antics of Rintarou Okabe, a self-proclaimed mad scientist that goes by the alias "Hououin Kyouma," as he essentially dicks around with time and subsequently deals with the consequences of his selfish actions. I'll be completely honest and say that the incredibly slow and random start to the anime threw me off so much that I re-watched the first episode 4 times over the course of 6 months before I could resolve to just pushing onward and finishing the anime. However, this slow start is balanced out by the fast-paced second half. By the end, it was answering questions that I never thought to ask, pointing out the significance of things that had long been discarded by my mind, and that sense of tying up loose ends is just the most refreshing feeling to have after dealing with so many time travel stories that are too lazy to clean up after themselves.
Unlike many time travel stories, especially in the world of anime, Steins;Gate has no noticeable inconsistencies objectively. I say objectively because this is a science fiction story, and that makes it really hard for everyone to agree on it. The thing is, none of us have experienced time travel in the way the characters in these science fiction stories have (and if you have experienced it, I'm very sorry for making assumptions), so there isn't a clear right or wrong way to write a time travel story. Obviously, if a story contradicts itself, something went wrong. But Steins;Gate seems to obey its own rules, and while a lot of people have made very compelling arguments that point out flaws in Steins;Gate's concept of time travel, they all make assumptions about how time travel works, and no one can really say for sure how things would change if we altered the past.
In the end, this isn't a science textbook, it's a science fiction anime. It's not supposed to be 100% believable, otherwise we wouldn't be able to watch it and say "wow, that was unbelievable!" I give the story a 10/10 because it was interesting, well-researched (many ideas are borrowed from other works of science fiction and played with), and overall just plain entertaining.
I really prefer talking about the art of a particularly spectacular-looking anime or else a particularly underwhelming-looking anime. Since the art in Steins;Gate is neither extremely good or extremely bad, I'll rate it an 8/10 for not influencing my opinion of the anime in either direction. Consider it a passing grade, basically where we should expect the art quality of anime to be in this day and age. Anything better would be remarkable.
I can't say much for the soundtrack, but the voice acting is awesome! Okabe's seiyuu is all kinds of talented, but everything good about the sound in this anime, and really, everything good about life in general, can be summed up in the maniacal laugh of Hououin Kyouma. I can't really speak for the English dub, and while I love Michael J. Tatum's work in Baccano, what I've heard of the dub sounds to be sorely lacking compared to the Japanese voices. Miyano Mamoru is just so cool! Sonuvabitch!
One thing of note about the soundtrack is the lack of one for a large portion of the anime. During quiet moments, rather than listening to quiet music, you're usually just listening to nothing. This is something that I've seen a few times, and I think it's pretty cool. It accentuates the importance of those scenes that do have music, and at the very least creates a nice contrast of mood, not between happy and sad music, but between silence and... not silence.
You should know that while not each and every character is the pinnacle of how great anime characters can be, they're all very interesting, entertaining, and Hououin Kyouma can handle being the pinnacle of just about everything.
But really, my rule for judging a character to be good is that I either like them or appreciate how much I don't like them. There are characters that I like and characters that I don't like in Steins;Gate, but all of them fit, and none of them are pointless and annoying. And yeah, Okabe is startlingly charismatic, and that can take an anime pretty far in the character department.
This anime made me laugh maniacally and cry silently. It also made me think, and it rewarded my thoughts by having closure and clarity, which left me more than satisfied. Easily a 10/10 anime, and now one of my favorites that I've seen!